Fractional Fourier transformation of Schwartz test functions

Abstract

In this paper we study the fractional Fourier transformation on the space S of Schwartz test functions, study some of its properties, and establish a two sided inverse for it. Also, we establish a convolution theorem for the fractional Fourier transform. We use duality to define fractional Fourier transform of tempered distributions. We define fractional convolution of a function and a tempered distribution and fractional convolution of tempered distributions, and show continuity of the convolution operators involved.

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Correspondence to Saleh Abdullah.

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Abdullah, S., Elshatarat, B. Fractional Fourier transformation of Schwartz test functions. Boll Unione Mat Ital 12, 599–611 (2019). https://doi.org/10.1007/s40574-019-00195-8

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Keywords

  • Fractional Fourier transform
  • Schwartz test functions
  • Tempered distribution

Mathematics Subject Classification

  • 46F12
  • 42A38